Question

In a triangle ABC BO AND CO are the bisector of angle ABC and angle ACB.if angle ABC=angle ACB and angle ABO equal to angle ACO show that angle CBO equal to angle BCO

Answer 1

Given :   In a triangle ABC BO and CO are the bisector of angle ABC and angle ACB .  angle ABC=angle ACB

To Find : show that angle CBO equal to angle BCO

Solution:

Δ ABC

∠ABC  = ∠ACB

Let say

∠ABC  = ∠ACB = 2k

BO and CO are the bisector of ∠ABC and ∠ACB

=> ∠ABO  =  ∠CBO  = (1/2)∠ABC  = (1/2)2k = k

∠ACO  =  ∠BCO  = (1/2)∠ACB = (1/2)2k = k  

∠CBO  =  ∠BCO   = k

QED

Hence proved

Learn More:

Make an angle of 75° and find its angle bisector. What are the ...

https://brainly.in/question/14728989

find the length of angle bisector of triangle abc where a = 6 CM B = 6 ...

https://brainly.in/question/8651539